One Dock to use with multiple laptops, Dell and other brands ?

I have some Precision 7520, HP ZBook G10 and Lenovo Thinkpad T580 laptops for various projects. I have a number of Dell docks - D3100, D6000 and TB16. I also have HP G2 and G4 docks, and a Targus 190. I have various ratings of power supply available. I have one desk. I'd really like to find a solution where I can have one dock and connect any of  my laptops to it and for it to "just work". And on Linux. I suspect this is asking for the impossible. I'm not looking for much ... two external 1920x1200 displays, mouse, keyboard, power and USB. I've tried them all and they all exhibit problems in one way or another.

I've read quite a bit, informative write ups by @jphughan, but struggled to find much on cross-compatibility.

I've had most success with the TB16 but it'll only charge the Dell laptops. Generally I find these new kind of docks always have some problem wheras the traditional style (Dell E-Port+II, Lenovo 40AJ) tend to "just work", right from the boot screen, but only with one specific laptop family.

Just wondered if there's any advice to help get something working across these laptop brands. I am not looking to buy anything else, just use what I have. If possible. If not, I'll just continue to use the traditional dock for the laptop that I use the most becuase it is reliable and "just works".

Thanks!